Solve for $x$ and $y$ using elimination. ${3x+2y = 29}$ ${-5x-2y = -43}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-2x = -14$ $\dfrac{-2x}{{-2}} = \dfrac{-14}{{-2}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {3x+2y = 29}\thinspace$ to find $y$ ${3}{(7)}{ + 2y = 29}$ $21+2y = 29$ $21{-21} + 2y = 29{-21}$ $2y = 8$ $\dfrac{2y}{{2}} = \dfrac{8}{{2}}$ ${y = 4}$ You can also plug ${x = 7}$ into $\thinspace {-5x-2y = -43}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ - 2y = -43}$ ${y = 4}$